A 3D adaptive mesh moving scheme

This paper presents an adaptive mesh moving technique for three-dimensional (3D) fluid flow problems that involve moving fluid boundaries and fluid–solid interfaces. Such mesh moving techniques are an essential ingredient of fluid–structure interaction methods that typically employ arbitrary Lagrangian–Eulerian (ALE) frameworks. In the ALE frame, the velocity field representing motion of the underlying continuum is integrated in the fluid flow equations. In the discretized setting, the velocity field of the underlying continuum gives rise to the mesh displacement field that needs to be solved for in addition to the flow equations and the structural equations. Emphasis in the present work is on the motion and deformation of 3D grids that are composed of linear tetrahedral and hexahedral elements in structured and unstructured configurations. The proposed method can easily be extended to higher-order elements in 3D. A variety of moving mesh problems from different fields of engineering are presented that show the range of applicability of the proposed method and the class of problems that can be addressed with it. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Tayfun E. Tezduyar,et al.  Automatic mesh update with the solid-extension mesh moving technique , 2004 .

[2]  Arif Masud,et al.  An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction , 2007 .

[3]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[4]  Tayfun E. Tezduyar,et al.  Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces , 1994 .

[5]  C. Bajaj,et al.  FINITE ELEMENT MESHING FOR CARDIAC ANALYSIS ∗ , 2004 .

[6]  Charbel Farhat,et al.  A three-dimensional torsional spring analogy method for unstructured dynamic meshes , 2002 .

[7]  C. Farhat,et al.  Torsional springs for two-dimensional dynamic unstructured fluid meshes , 1998 .

[8]  S. Mittal,et al.  A finite element study of incompressible flows past oscillating cylinders and aerofoils , 1992 .

[9]  Arif Masud,et al.  Effects of Mesh Motion on the Stability and Convergence of ALE Based Formulations for Moving Boundary Flows , 2006 .

[10]  Boniface Nkonga,et al.  On the conservative and accurate CFD approximations for moving meshes and moving boundaries , 2000 .

[11]  Tayfun E. Tezduyar,et al.  Advanced mesh generation and update methods for 3D flow simulations , 1999 .

[12]  T. Tezduyar,et al.  Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements , 2003 .

[13]  T. Tezduyar,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests , 1992 .

[14]  Thomas J. R. Hughes,et al.  A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems , 1997 .

[15]  Tayfun E. Tezduyar,et al.  Shear-Slip Mesh Update in 3D Computation of Complex Flow Problems with Rotating Mechanical Components , 2001 .

[16]  Carlo L. Bottasso,et al.  The ball-vertex method: a new simple spring analogy method for unstructured dynamic meshes , 2005 .

[17]  Arif Masud,et al.  A Multiscale/stabilized Formulation of the Incompressible Navier–Stokes Equations for Moving Boundary Flows and Fluid–structure Interaction , 2006 .

[18]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[19]  Marek Behr,et al.  The Shear-Slip Mesh Update Method , 1999 .

[20]  Yong Zhao,et al.  A general method for simulation of fluid flows with moving and compliant boundaries on unstructured grids , 2003 .

[21]  Tayfun E. Tezduyar,et al.  Simulation of multiple spheres falling in a liquid-filled tube , 1996 .

[22]  J. Brackbill,et al.  Adaptive zoning for singular problems in two dimensions , 1982 .

[23]  R. T. McLay,et al.  Automatic Remeshing Scheme for Modeling Hot Forming Process , 1986 .

[24]  S. Mittal,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. II: Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders , 1992 .

[25]  Yongjie Zhang,et al.  3D Finite Element Meshing from Imaging Data. , 2005, Computer methods in applied mechanics and engineering.

[26]  Charbel Farhat,et al.  Multidisciplinary Simulation of the Maneuvering of an Aircraft , 2001, Engineering with Computers.

[27]  J. Hyvärinen,et al.  An Arbitrary Lagrangian-Eulerian finite element method , 1998 .

[28]  Marek Behr,et al.  Stabilized finite element methods for incompressible flows with emphasis on moving boundaries and interfaces , 1992 .

[29]  Arif Masud,et al.  A multiscale finite element method for the incompressible Navier-Stokes equations , 2006 .